A pet owner can also put their pet down if it costs too much… I mean, that comparison is really too much. Forget infanticide, putting your pet to sleep is legal at any age, as long as they’re in your care. A chilling thought when applied to children.
The distinction that pro-choicers who advance this argument are missing (besides the obvious distinction between a parasite and a human being) is a duty of care. Judith Jarvis Thomson has a somewhat similar thought experiment to this called “The Violinist” in 1971: you can get the gist of it here: en.wikipedia.org/wiki/Violinist_(thought_experiment). It’s both a clever and incredibly callous argument in that it doesn’t matter whether the baby is a human being.
The reason it’s legal to surgically detach the violinist in that hypothetical is because the person has no reasonable legal duty to care. We can’t be expected to feed every poor child on Earth, but we **are **legally responsible for feeding our own. If it is your child, and you haven’t turned over those rights via adoption (or something similar), you have a legal duty to provide for the kid, even things like medical care. Hopefully, that makes sense - it’s only sort of related, but I think it’s important. He/She’s not just “a” child, it’s “her” child, and she’s responsible for the kid, whether she wants to be or not.